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------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- G N A T . M B B S _ D I S C R E T E _ R A N D O M --
-- --
-- B o d y --
-- --
-- Copyright (C) 1992-2013, Free Software Foundation, Inc. --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
with Ada.Calendar;
with Interfaces; use Interfaces;
package body GNAT.MBBS_Discrete_Random is
package Calendar renames Ada.Calendar;
Fits_In_32_Bits : constant Boolean :=
Rst'Size < 31
or else (Rst'Size = 31
and then Rst'Pos (Rst'First) < 0);
-- This is set True if we do not need more than 32 bits in the result. If
-- we need 64-bits, we will only use the meaningful 48 bits of any 64-bit
-- number generated, since if more than 48 bits are required, we split the
-- computation into two separate parts, since the algorithm does not behave
-- above 48 bits.
-- The way this expression works is that obviously if the size is 31 bits,
-- it fits in 32 bits. In the 32-bit case, it fits in 32-bit signed if the
-- range has negative values. It is too conservative in the case that the
-- programmer has set a size greater than the default, e.g. a size of 33
-- for an integer type with a range of 1..10, but an over-conservative
-- result is OK. The important thing is that the value is only True if
-- we know the result will fit in 32-bits signed. If the value is False
-- when it could be True, the behavior will be correct, just a bit less
-- efficient than it could have been in some unusual cases.
--
-- One might assume that we could get a more accurate result by testing
-- the lower and upper bounds of the type Rst against the bounds of 32-bit
-- Integer. However, there is no easy way to do that. Why? Because in the
-- relatively rare case where this expression has to be evaluated at run
-- time rather than compile time (when the bounds are dynamic), we need a
-- type to use for the computation. But the possible range of upper bound
-- values for Rst (remembering the possibility of 64-bit modular types) is
-- from -2**63 to 2**64-1, and no run-time type has a big enough range.
-----------------------
-- Local Subprograms --
-----------------------
function Square_Mod_N (X, N : Int) return Int;
pragma Inline (Square_Mod_N);
-- Computes X**2 mod N avoiding intermediate overflow
-----------
-- Image --
-----------
function Image (Of_State : State) return String is
begin
return Int'Image (Of_State.X1) &
',' &
Int'Image (Of_State.X2) &
',' &
Int'Image (Of_State.Q);
end Image;
------------
-- Random --
------------
function Random (Gen : Generator) return Rst is
S : State renames Gen.Writable.Self.Gen_State;
Temp : Int;
TF : Flt;
begin
-- Check for flat range here, since we are typically run with checks
-- off, note that in practice, this condition will usually be static
-- so we will not actually generate any code for the normal case.
if Rst'Last < Rst'First then
raise Constraint_Error;
end if;
-- Continue with computation if non-flat range
S.X1 := Square_Mod_N (S.X1, S.P);
S.X2 := Square_Mod_N (S.X2, S.Q);
Temp := S.X2 - S.X1;
-- Following duplication is not an error, it is a loop unwinding
if Temp < 0 then
Temp := Temp + S.Q;
end if;
if Temp < 0 then
Temp := Temp + S.Q;
end if;
TF := Offs + (Flt (Temp) * Flt (S.P) + Flt (S.X1)) * S.Scl;
-- Pathological, but there do exist cases where the rounding implicit
-- in calculating the scale factor will cause rounding to 'Last + 1.
-- In those cases, returning 'First results in the least bias.
if TF >= Flt (Rst'Pos (Rst'Last)) + 0.5 then
return Rst'First;
elsif not Fits_In_32_Bits then
return Rst'Val (Interfaces.Integer_64 (TF));
else
return Rst'Val (Int (TF));
end if;
end Random;
-----------
-- Reset --
-----------
procedure Reset (Gen : Generator; Initiator : Integer) is
S : State renames Gen.Writable.Self.Gen_State;
X1, X2 : Int;
begin
X1 := 2 + Int (Initiator) mod (K1 - 3);
X2 := 2 + Int (Initiator) mod (K2 - 3);
for J in 1 .. 5 loop
X1 := Square_Mod_N (X1, K1);
X2 := Square_Mod_N (X2, K2);
end loop;
-- Eliminate effects of small Initiators
S :=
(X1 => X1,
X2 => X2,
P => K1,
Q => K2,
FP => K1F,
Scl => Scal);
end Reset;
-----------
-- Reset --
-----------
procedure Reset (Gen : Generator) is
S : State renames Gen.Writable.Self.Gen_State;
Now : constant Calendar.Time := Calendar.Clock;
X1 : Int;
X2 : Int;
begin
X1 := Int (Calendar.Year (Now)) * 12 * 31 +
Int (Calendar.Month (Now) * 31) +
Int (Calendar.Day (Now));
X2 := Int (Calendar.Seconds (Now) * Duration (1000.0));
X1 := 2 + X1 mod (K1 - 3);
X2 := 2 + X2 mod (K2 - 3);
-- Eliminate visible effects of same day starts
for J in 1 .. 5 loop
X1 := Square_Mod_N (X1, K1);
X2 := Square_Mod_N (X2, K2);
end loop;
S :=
(X1 => X1,
X2 => X2,
P => K1,
Q => K2,
FP => K1F,
Scl => Scal);
end Reset;
-----------
-- Reset --
-----------
procedure Reset (Gen : Generator; From_State : State) is
begin
Gen.Writable.Self.Gen_State := From_State;
end Reset;
----------
-- Save --
----------
procedure Save (Gen : Generator; To_State : out State) is
begin
To_State := Gen.Gen_State;
end Save;
------------------
-- Square_Mod_N --
------------------
function Square_Mod_N (X, N : Int) return Int is
begin
return Int ((Integer_64 (X) ** 2) mod (Integer_64 (N)));
end Square_Mod_N;
-----------
-- Value --
-----------
function Value (Coded_State : String) return State is
Last : constant Natural := Coded_State'Last;
Start : Positive := Coded_State'First;
Stop : Positive := Coded_State'First;
Outs : State;
begin
while Stop <= Last and then Coded_State (Stop) /= ',' loop
Stop := Stop + 1;
end loop;
if Stop > Last then
raise Constraint_Error;
end if;
Outs.X1 := Int'Value (Coded_State (Start .. Stop - 1));
Start := Stop + 1;
loop
Stop := Stop + 1;
exit when Stop > Last or else Coded_State (Stop) = ',';
end loop;
if Stop > Last then
raise Constraint_Error;
end if;
Outs.X2 := Int'Value (Coded_State (Start .. Stop - 1));
Outs.Q := Int'Value (Coded_State (Stop + 1 .. Last));
Outs.P := Outs.Q * 2 + 1;
Outs.FP := Flt (Outs.P);
Outs.Scl := (RstL - RstF + 1.0) / (Flt (Outs.P) * Flt (Outs.Q));
-- Now do *some* sanity checks
if Outs.Q < 31
or else Outs.X1 not in 2 .. Outs.P - 1
or else Outs.X2 not in 2 .. Outs.Q - 1
then
raise Constraint_Error;
end if;
return Outs;
end Value;
end GNAT.MBBS_Discrete_Random;
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